Answer: umm please provide the answers you can chose then maybe i can help
Step-by-step explanation:
Which of the following tables represents a linear function?
The first table in the question with the values(2,-3)(2,-2)(2,-1)(2,0)(2,1)represents the linear function.
What is linear function?A linear function is a type of mathematical function that has a constant rate of change or slope. This means that the function produces a straight line when graphed on a coordinate plane.
A linear function can be represented using the general form:
f(x) = mx + b
where m is the slope or rate of change, and b is the y-intercept or the point where the line intersects the y-axis.
In the given question, Option (1),
(2,-3)(2,-2)(2,-1)(2,0)(2,1).
If plotted on graph forms a straight line.
But all the other three options does not form a straight line.
Therefore, its a linear function.
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quiz 10 147 cars were sold during the month of april. 81 had air conditioning and 82 had automatic transmission. 54 had air conditioning only, 55 had automatic transmission only, and 11 had neither of these extras. what is the probability that a randomly selected car had automatic transmission or air conditioning or both?
The probability that a randomly selected car had automatic transmission or air conditioning or both is 0.92517.
Total number of cars sold, n = 147
Let A denotes the car is air conditioning.
And B denotes the car is automatic message transmission.
A = 81
B = 82
Number of cars that neither of these extras = 11
Only A = 54
Only B = 55
Now,
P(A ∩ B') = A/n
P(A ∩ B') = 81/147
P(A ∩ B') = 0.551
P(A' ∩ B') = 11/147
P(A' ∩ B') = 0.07483
The probability that a randomly selected car had automatic transmission or air conditioning or both is:
P(A ∪ B) = 1 - P(A' ∩ B')
P(A ∪ B) = 1 - 0.07483
P(A ∪ B) = 0.92517
The likelihood that an automobile chosen at random has either an automatic gearbox, air conditioning, or both is 0.92517.
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You have a summer job cleaning swimming pools. Pools are cleaned with pumps and filters. Water is pumped into the filter to remove particles that make the water less clear. A unit called NTU¹ is used to measure how clear water is. For example, in a pool: . 0.1 NTU is considered clean, safe water. 0.9 NTU has too many particles to be clean, safe water. • In this task you will determine how long a pump needs to operate in order to clean the water in a large pool. Nephelometric Turbidity Units 3 JEWELEAH In the same large pool, the measurement is currently 0.8 NTU. When the pool opens in the morning, the measurement needs to be 0.4 NTU. Your manager claims that this will be done if you run the pump for 4 hours because 10% is 0.10 and 0.8 -0.10 0.10 - 0.10 - 0.10 = 0.4. He is incorrect. Complete the chart below to determine what the NTU measurement would be after running the pump for 4 hours. Round your answers to the nearest hundredth. Hours 0 1 2 3 4 hp NTU 0.80
After running the pump for 4 hours, the NTU measurement would be approximately 0.52.
How to solve this problemTo determine the NTU measurement after running the pump for 4 hours, we need to consider that the pump reduces the NTU by 10% each hour.
Here's the chart with the NTU values for each hour, rounded to the nearest hundredth:
Hours | NTU
0 | 0.80
1 | 0.72 (0.80 * (1 - 0.10) = 0.80 * 0.9)
2 | 0.65 (0.72 * (1 - 0.10) = 0.72 * 0.9)
3 | 0.58 (0.65 * (1 - 0.10) = 0.65 * 0.9)
4 | 0.52 (0.58 * (1 - 0.10) = 0.58 * 0.9)
After running the pump for 4 hours, the NTU measurement would be approximately 0.52.
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If x and b are the roots of ax^2 - bx + c then calculate x + b
Answer:
Step-by-step explanation:
Find the area of the triangle below.
20 cm
5 cm
13 cm
Answer:
19
Step-by-step explanation:
20+5+13 / 2 = 19
A roofer requires 8 hours to shingle a roof. After the roofer and
an apprentice work on a roof for 2 hours, the roofer moves on to
another job. The apprentice requires 10 more hours to finish the
job. How long would it take the apprentice, working alone, to do
the job?
The apprentice can complete the job alone in approximately 11.43 hours (rounded to two decimal places). We can calculate it in the following manner.
Let's assume that the apprentice can complete the job alone in "x" hours.
In 2 hours, the roofer completes a fraction of the job which is equivalent to:
(2/8) = 1/4 of the job.
This means that the remaining fraction of the job that the apprentice has to complete is:
1 - 1/4 = 3/4 of the job.
The apprentice completes this remaining fraction of the job in 10 hours, so the rate at which he works is:
(3/4) of the job / 10 hours = 3/40 of the job per hour.
Since we know that the apprentice can complete the entire job alone in "x" hours, we can set up the equation:
1 job / x hours = 3/40 of the job per hour * (x - 10) hours
Simplifying this equation, we get:
x = 80/7
Therefore, the apprentice can complete the job alone in approximately 11.43 hours (rounded to two decimal places).
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in each case, from the coordinates of the given point, write the rule of the quadratic function
a: (6, 216)
b: (-4, 128)
c: (7, -490)
d: (0.5, 8)
e: (-4.5, -40.5)
f: (8, 16)
g: 8, 1/2)
h: 9, 275.4)
I: (10, -48)
a: y = 6x²
b: y = 8x² + 64x + 128
c: y = -23x² + 322x - 1056
d: y = 64x² - 64x + 8
e: y = -9x² - 81
f: y = -4x² + 64
g: y = -2x² + 8x
h: y = 1.4x² - 25.2x + 118.4
i: y = -18x² + 180x - 680
please help me with this
Answer:
Step-by-step explanation:
No of blue marbles=4
No of red marbles=3
Total number of marbles = 7
Probability of getting blue marbles = 4/7
Probability of getting red marbles= 3/7
How would you solve this integral? Supposedly, you take the U sub of x/3, and then resubtitute after solving for du and dx getting 3/sqrt(9-9u^2)du which you then take the integral of to get the standard arcsin(u). Is there a more general way of doing this, or do I have to remember this standard integral?
Answer:
Step-by-step explanation:
You have a jar of 20 jellybeans, and 4 are red. Which fraction represents the probability that you will pick a red jellybean out of the jar?
A
4
2
0
20
4
B
1
6
2
0
20
16
C
2
0
4
4
20
D
2
0
1
6
16
20
There are 4 red jellybeans in a jar of 20 total. The probability that you will choose a red jellybean from the jar is represented by the fraction 4/20.
The probability of picking a red jellybean out of the jar is the number of red jellybeans in the jar divided by the total number of jellybeans in the jar.
So, P(red jellybean) = number of red jellybeans / total number of jellybeans
= 4/20
= 1/5
Therefore, the fraction that represents the probability of picking a red jellybean out of the jar is 4/20.
The complete question is:-
You have a jar of 20 jellybeans, and 4 are red. Which fraction represents the probability that you will pick a red jellybean out of the jar?
A) 4/20
B) 16/20
C) 20/4
D) 20/16
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a study wants to determine the average tuition that san jose state undergraduate students would pay per semester. each student in the following samples is asked how much tuition he or she paid for the fall semester. what is the type of sampling in each case?
The type of sampling used in each case of the students to pay tuition fee for the fall semester is simple random sampling.
Simple random sampling is the method that was applied in this instance. Each person in the population has an equal probability of being chosen for the sample when using simple random sampling. In this instance, the amount of tuition each participant in the sample paid for the autumn semester was questioned.
The type of sampling in the next case is stratified sampling. After classifying the students into freshmen, sophomores, juniors, or seniors, 25 students from each group are chosen. The sample will be representative of each group thanks to this technique.
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Complete question is:
A study wants to determine the average tuition that san jose state undergraduate students would pay per semester. each student in the following samples is asked how much tuition he or she paid for the fall semester. what is the type of sampling in each case?
A sample of 100 undergraduate San Jose State students is taken by organizing the students’ names by classification (freshman, sophomore, junior, or senior), and then selecting 25 students from each.
what type of error occurs if you fail to reject h0 when, in fact, it is not true? group of answer choices either type i or type ii, depending on the level of significance type ii type i either type i or type ii, depending on whether the test is one-tailed or two-tailed
The type of error depends on the level of significance and whether the test is one-tailed or two-tailed.
The type of error occurs if you fail to reject H0 when, in fact, it is not true.
The type of error that occurs when one fails to reject H0 when, in reality, it is false is type II error.
Type II error is an error in which one accepts a null hypothesis that should be rejected.
This type of error is the opposite of type I error, where one rejects a null hypothesis that is true.
A type II error is a serious issue because it suggests that a significant difference exists, but the statistical test fails to detect it.
There are two types of errors associated with hypothesis testing, type I and type II errors, depending on the significance level of the test.
A type I error occurs when the null hypothesis is rejected when it is true.
A type II error happens when the null hypothesis is not rejected when it is false.
A type I error, also known as an alpha error, is caused by rejecting the null hypothesis when it is true.
It occurs when the significance level is set too high or when a statistical test is not performed correctly.
A type I error occurs when the observed value lies in the rejection region of the null hypothesis, and we reject the null hypothesis even though it is true.
In conclusion, when one fails to reject H0 when it is false, a type II error occurs. On the other hand, when one rejects H0 when it is true, a type I error occurs.
The type of error depends on the level of significance and whether the test is one-tailed or two-tailed.
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each serving of these crackers provides 120 calories (kcal) and 0.5 grams of saturated fat. what percentage of calories comes from saturated fat?
The percentage of calories that comes from saturated fat in each serving of these crackers is 0.4%
To calculate the percentage of calories that come from saturated fat, we need to first determine how many calories come from saturated fat in one serving of crackers.
We know that each serving of crackers provides 120 calories, and 0.5 grams of saturated fat. We can convert the amount of saturated fat from grams to calories by multiplying it by 9 (since 1 gram of fat provides 9 calories).
0.5 grams of saturated fat x 9 calories per gram = 4.5 calories from saturated fat
Therefore, out of the 120 total calories in one serving of crackers, 4.5 calories come from saturated fat.
To find the percentage of calories that come from saturated fat, we can divide the number of calories from saturated fat by the total number of calories in one serving of crackers, and then multiply by 100.
(4.5 calories from saturated fat / 120 total calories) x 100 = 0.0375 x 100 = 0.4%
Therefore, each serving of crackers provides 0.4% of calories from saturated fat.
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Caleb bought 26.4kg of fish from a cold store. His sister, Moesha also bought 2.4kg of meat less than her brother, Caleb. H ow many kilograms of meat did they buy altogether?
Caleb and Moesha bought a total of 50.4 kg of meat.
Word problemCaleb bought 26.4 kg of fish from the cold store.
Moesha bought 2.4 kg less than Caleb, which means she bought 26.4 kg - 2.4 kg = 24 kg of meat.
Therefore, the total amount of meat they bought together is:
26.4 kg + 24 kg = 50.4 kg
So Caleb and Moesha bought a total of 50.4 kg of meat.
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What are the value of x and the measure of ZE to the nearest degree?
The correct answer is: [tex]x=\sqrt{28}, m \angle E=37^{\circ}[/tex]. Thus, option D is correct by using Pythagorean theorem.
What is trigonometry and the properties of right triangles?In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be represented as:
[tex]c^2 = a^2 + b^2[/tex]
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Given that x is the hypotenuse of the right triangle and [tex]$x = \sqrt{28}$[/tex], we can use the Pythagorean theorem to find the lengths of the other two sides. Since x is the hypotenuse, it will be equal to c in the Pythagorean theorem equation. Plugging in the values, we get:
[tex](\sqrt{28})^2 = a^2 + b^2[/tex]
[tex]28 = a^2 + b^2[/tex]
Now, we are given the measure of [tex]\angle E[/tex] which is [tex]37^{\circ}[/tex]. In a right triangle, one angle is always [tex]90^{\circ}[/tex], so the sum of the measures of the other two angles will be [tex]90^{\circ}[/tex] . Therefore, angle must be one of the acute angles of the right triangle.
To find the value of a and b, we can use trigonometric ratios. In a right triangle, the sine, cosine, and tangent ratios are commonly used.
For [tex]$\angle E$[/tex], we can use the sine ratio, which is defined as:
[tex]$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$[/tex]
In our case, the opposite side of [tex]$\angle E$ is $a$[/tex] and the hypotenuse is x. Plugging in the values, we get:
[tex]$\sin(37^{\circ}) = \frac{a}{\sqrt{28}}$[/tex]
Solving for a, we get:
[tex]$a = \sin(37^{\circ}) \cdot \sqrt{28}$[/tex]
Similarly, we can use the cosine ratio to find b. The cosine ratio is defined as:
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
In our case, the adjacent side of angle E is b and the hypotenuse is x. Plugging in the values, we get:
[tex]$\cos(37^{\circ}) = \frac{b}{\sqrt{28}}$[/tex]
Solving for b, we get:
[tex]b = \cos(37^{\circ}) \cdot \sqrt{28}[/tex]
Therefore, , the correct answer is The correct answer is: [tex]x=\sqrt{28}, m \angle E=37^{\circ}[/tex], as given in option [tex]x=\sqrt{28},[/tex] m [tex]\angle E=37^{\circ}$.[/tex]
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A summary of two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Unix Co UNX 8.15 8.78 8.06
Cubix Inc CBX 15.65 16.92 14.35
Suppose you purchase 65 shares of Unix stock and 50 shares of Cubix stock on Day 1 at the closing price. Which day, during the following two days, would be best to sell both stocks on, and by how much?
The best day to sell both stocks would be Day 2, as both stocks saw an increase in closing price. The total profit from selling both stocks on Day 2 would be $104.65.
What is opening and closing price?The stock's trading price at the close of a trading day is known as the closing price. Up to the start of the following trading session, this is the stock's most recent price. The market hours for shares are 9:15 AM to 3:30 PM. In the case of equities, the closing price is determined as the weighted average price of the previous 30 minutes, or from 3:00 to 3:30 PM.
The price at which a stock first trades on an exchange on a trading day is known as the opening price. The market hours for shares are 9:15 AM to 3:30 PM. Nonetheless, the pre-market window, which runs from 9:00 AM to 9:08 AM, is when the exchange begins accepting orders.
According to the given information,
For Unix Co the change in closing price:
From Day 1 to Day 2:
8.78 - 8.15 = 0.63,
From Day 1 to Day 3:
8.06 - 8.15 = -0.09.
Now, for Cubix Inc we have:
Day 1 to Day 2:
16.92 - 15.65 = 1.27
Day 1 to Day 3:
14.35 - 15.65 = -1.30.
Thus, the best day to sell both stocks would be Day 2, as both stocks saw an increase in closing price.
Now, when we sell 65 shares of Unix Co at day 2 at 8.78 we have:
(8.78 - 8.15) x 65 = $41.15
For 50 shares of Cubix Inc:
(16.92 - 15.65) x 50 = $63.50.
Hence, the total profit from selling both stocks on Day 2 would be $41.15 + $63.50 = $104.65.
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PRETTY PLEASE WITH A CHERRY ON TOP PLEASE HELP URGENT ASAP!! WILL MARK BRANLIEST. SIMPLE PROBLEM GEOMETRY BUT I CANT SOLVE IT HELP!!
Find the center of this circle. Label the center as point A
if there is a formula please put it in the explanation.
Answer:
Draw a line perpendicular (90°) to the chord GH, half way along it's length
Now you know why it's easier to pick an easy length to start with. Make sure it goes past where the center of the circle should be. You can go straight across if that's easier.
Do the same for chord JK
The point of intersection of the 2 chord's perpendicular line is the centre of the circle
This should be enough to find the center of the circle, but you can add more chords to make sure
pls mark me as brainliest :)
t-test: are the average vit. d levels for sections 1 (control group) and 2 (experimental group receiving vit. d supplements) significantly different?
If there is a significant difference in the average vitamin D levels between the control group and the experimental group receiving vitamin D supplements then t-test can be used to determine the significance of the difference.
To determine if the average vitamin D levels for sections 1 and 2 are significantly different, a t-test can be performed. The null hypothesis would be that there is no significant difference in the average vitamin D levels between the two groups, while the alternative hypothesis would be that there is a significant difference.
The t-test would provide a p-value, which can be used to determine the significance of the difference between the two groups. If the p-value is less than the chosen level of significance (usually 0.05), then it can be concluded that there is a significant difference in the average vitamin D levels between the two groups.
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Use the image to answer the question.
Determine the type of dilation shown and the scale factor used.
Enlargement with scale factor of 1.5
Enlargement with scale factor of 2
Reduction with scale factor of 1.5
Reduction with scale factor of 2
Answer:
The correct answer is enlargement scale factor of 1.5.
Step-by-step explanation:
the reason for this is that if you divide the D' numbers by the D numbers you get 1.5
so 8×1.5=12
6×1.5=9
any scale factor 0-1 is a reduction. Greater than 1 (like this case here) is an enlargement. as you can see the after image D' is bigger than the pre image D
I hope this helps :)
A scale drawing of a famous statue uses a scale factor of 250:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
The actual height of the statue is 0.0048 feet or 0.0576 inches.
What is scale factor?The scale factor is a way to compare figures with similar appearances but distinct scales or measurements. Consider two circles that resemble one another but may have different diameters. The scale factor indicates how much a figure has increased or decreased from its initial value.
If the scale factor is 250:1, it means that every 250 units in the actual object correspond to 1 unit in the drawing. In this case, we know the height of the drawing is 1.2 feet, which is 1 unit in the drawing.
To find the actual height of the statue, we can use the scale factor to set up a proportion:
250 units (actual height) : 1 unit (drawing height) = x (actual height) : 1.2 feet (drawing height)
Cross-multiplying:
250x = 1.2
Dividing both sides by 250:
x = 0.0048
Therefore, the actual height of the statue is 0.0048 feet or 0.0576 inches.
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Can someone help me???? Please
Answer:
1) a = 1, b = -8, c = 17; Vertex: (4, 1)
2) a = -1, b = -2. c = -2; Vertex: (-1, -1)
3) a = -1, b = 6, c = -8; Vertex: (3, 1)
4) a = -3, b = 6, c = 0; Vertex: (1, 3)
5) a = -2, b = -16, c = -31; Vertex: (-4, 1)
6) a = -1/2 or -0.5, b = -4, c = -6; Vertex: (-4, 2)
Step-by-step explanation:
The quadratic functions listed are all in standard form:
y = ax² + bx + c
where a, b, and c, are coefficients for each of the terms.
Vertex
To find the vertex of a parabolic equation in standard form. Calculate -b/2a. This will be your x-coordinate. Then substitute this back into f(x) to obtain the y-coordinate; The calculated point is your vertex.
1) x = - b / 2a = - (-8) / 2 (1) = 8 / 2 = 4
f(4) = 4² - 8 (4) + 17 = 16 - 32 + 17 = 1
Vertex: (4, 1)
2) x = -b / 2a = - (-2) / 2 (-1) = 2 / (-2) = -1
f(-1) = - (-1)² - 2 (-1) - 2 = -1 + 2 - 2 = -1
Vertex: (-1, -1)
3) x = - b / 2a = - (6) / 2 (-1) = -6 / -2 = 3
f(3) = - (3)² + 6 (3) -8 = -9 + 18 - 8 = 1
Vertex: (3, 1)
4) x = - b / 2a = - (6) / 2 (-3) = -6 / -6 = 1
f(1) = -3 (1)² + 6 (1) = -3 + 6 = 3
Vertex: (1, 3)
5) x = - b / 2a = - (-16) / 2(-2) = 16 / -4 = -4
f(-4) = -2 (-4)² - 16 (-4) - 31 = -32 + 64 - 31 = 1
Vertex: (-4, 1)
6) x = - b / 2a = - (-4) / 2 (-0.5) = 4 / -1 = -4
f (-4) = (-0.5) (-4)² - 4 (-4) - 6 = -8 + 16 - 6 = 2
Vertex: (-4, 2)
You start at (4, -4). You move up 6 units. Where do you end?
Answer:
You end at the coordinates (4, 2)
The point P =
in simplest form?
5) lies on the unit circle shown below. What is the value of x
Thus, the value of x in obtained in the simplest form for the unit circle is: x = -√5/3.
Explain about the unit circle:A circle with a radius of one unit and a centre at the origin is referred to as a unit circle just on Cartesian Plane (0, 0). When working with trigonometric functions including angle measurements, the unit circle is a useful tool that makes reference much simpler.
The equation of unit circle, radius r = 1 unit. :
x² + y² = 1.
For the given point P (x, 2/3), we can solve for x by substituting each quantity into the equation.
x² + (2/3)² = 1
x² + 4/9= 1.
Subtract 4/9 from both side.
x² = 5/9.
Taking square root on both side.
x = √5/3
x = -√5/3
Thus, the value of x in obtained in the simplest form for the unit circle is: x = -√5/3.
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Complete question:
the point P=(x,2/3) lies on the unit circle shown below . what is the value of x in simplest form?
The diagram is attached.
Diane has 4 markers. Her best friend ally gives her 12 more pencils. How many pencils does she have?
Answer:
16
Step-by-step explanation:
4 + 12= 16
4 + 2 = 6
Add a 1 in front
which statement is not true about the data shown by the box-and-whisker plot below? the data point 5 lies outside the range of the data. half the data lies between 37 and 51. the range is 57. one fourth of the data is greater than 51.
The statement "the data point 5 lies outside the range of the data" is not true about the data shown by the box-and-whisker plot below.
To understand why the statement is not true, we need to interpret the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom and top of the box indicating the 25th and 75th percentiles, respectively. The line inside the box represents the median. The whiskers represent the range of the data, with the endpoints of the whiskers indicating the minimum and maximum values, unless there are outliers.
Looking at the plot, we can see that the minimum value is 5, which is within the whisker range. Therefore, the statement "the data point 5 lies outside the range of the data" is not true. The statement "half the data lies between 37 and 51" is true, as the bottom and top of the box represent the 25th and 75th percentiles, respectively. The statement "the range is 57" is true, as the distance between the minimum and maximum values is 57. The statement "one fourth of the data is greater than 51" is also true, as the top of the box represents the 75th percentile.
Therefore, the correct statement is "the data point 5 lies within the range of the data."
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In Mrs. Franklin's kindergarten class, children make handprints in a round clay mold for their parents. The mold has a radius of 2 inches. What is the mold's circumference?
Answer:
4π (approx. 12.57) inches
Step-by-step explanation:
Equation to find circumference of a circle is πd, where d is the diameter of the circle.
d = 2r (radius)
d = 4
Circumference = πd
Circumference = 4π (inches)
Circumference ≈ 12.57 (inches)
I NEED HELP! BRAINLEST!
Answer:
Area of the shape = 62.135 (units^2)
Step-by-step explanation:
To start, divide the shape into simpler parts.
A triangle (4 by 6)
A Rectangle (6 by 6)
A half Circle (Radius of 3) - take the height (6) and divide it by 2 (= 3)
First get the area of the Triangle. Base x Height / 2
4 x 6 = 24; 24 / 2 = 12;
Area of the Triangle is 12
Second get the area of the Rectangle. Length x Width
6 x 6 = 36
Area of the Rectangle is 36
Third get the area of the circle Pie x Radius ^2 (squared)
3.14 x (3 ^2) = 28.27
Now take the area of the whole circle and divide it by 2 to get the half circle
28.27 / 2 = 14.135; Area of the half Circle is 14.135
Add up all the areas to get the total for your shape.
12 + 36 + 14.135 = 62.135
Robert is on a diet to lose weight before his Spring Break trip to the Bahamas. He is losing weight at a rate of 2 pounds per week. After 6 weeks, he weighs 205 pounds. Write and solve a linear equation to model this situation. There should be at least 3 lines of work.
Answer: Let x be the number of weeks since Robert started his diet, and let y be his weight in pounds. We know that he is losing weight at a rate of 2 pounds per week, so the slope of the line is -2 (negative because he is losing weight). We also know that after 6 weeks, his weight is 205 pounds, so we have the point (6, 205).
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - 205 = -2(x - 6)
Simplifying this equation gives:
y - 205 = -2x + 12
y = -2x + 217
Therefore, the equation that models Robert's weight loss is y = -2x + 217.
To find how much weight Robert will lose after 8 weeks, we substitute x = 8 into the equation:
y = -2(8) + 217
y = 201
Therefore, Robert will weigh 201 pounds after 8 weeks on his diet.
To check that this answer is reasonable, we can use the information that Robert is losing weight at a rate of 2 pounds per week. In 8 weeks, he would have lost:
2 pounds/week x 8 weeks = 16 pounds
205 pounds - 16 pounds = 189 pounds
Since 201 pounds is more than 189 pounds, our answer of 201 pounds after 8 weeks is reasonable.
So the completed work is:
Let x be the number of weeks since Robert started his diet, and let y be his weight in pounds.
We know that he is losing weight at a rate of 2 pounds per week, so the slope of the line is -2 (negative because he is losing weight).
We also know that after 6 weeks, his weight is 205 pounds, so we have the point (6, 205).
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - 205 = -2(x - 6)
Simplifying this equation gives:
y - 205 = -2x + 12
y = -2x + 217
Therefore, the equation that models Robert's weight loss is y = -2x + 217.
To find how much weight Robert will lose after 8 weeks, we substitute x = 8 into the equation:
y = -2(8) + 217
y = 201
Therefore, Robert will weigh 201 pounds after 8 weeks on his diet.
Step-by-step explanation:
Can someone help me???? Please just answers
All the quadratic functions but f(x) = 3x^2-24x+46 and f(x) = 2x^2+8x+5 have no real solutions
Solving the functionsFunction 7
Given that
f(x) = -2x^2 + 12x - 22
Using the discriminant D = b^2 - 4ac, we have
D = 12^2 - 4 * -2 * -22
D = -32
This is less than 0
The equation has no real solution
Function 8
Given that
f(x) = x^2-8x+20
Using the discriminant D = b^2 - 4ac, we have
D = -8^2 - 4 * 1 * 20
D = -16
This is less than 0
The equation has no real solution
Function 9
Given that
f(x) = 3x^2-24x+46
By the use of graph, we have
x = 3.184 and x = 4.816
Function 10
Given that
f(x) = x^2+2x+2
Using the discriminant D = b^2 - 4ac, we have
D = 1^2 - 4 * 2 * 2
D = -15
This is less than 0
The equation has no real solution
Function 11
Given that
f(x) = -1/2x^2+4x-10
Using the discriminant D = b^2 - 4ac, we have
D = 4^2 - 4 * -1/2 * -10
D = -4
This is less than 0
The equation has no real solution
Function 12
Given that
f(x) = 2x^2+8x+5
By the use of graph, we have
x = -3.225 and x = -0.775
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The graph attached shows the position of a race car as it tests out a new engine.
a. What is the distance traveled by the car between 1 and 9 seconds?
b. What is the average speed of the car between 1 and 9 seconds? (Answer in km/s.)
c. Describe how the speed of the car changes throughout its test run.
d. If you had a graph of velocity versus time for this test, what would be the total area under the curve?
Please show all work
a) The distance traveled by the car is 240 km, b) the average speed of the car is 30 km/s, c) the speed of the car changes from increasing to constant to decreasing, d) and the total area under the curve 240 km/s.
a. To find the distance traveled by the car between 1 and 9 seconds, we need to find the area under the curve of the velocity-time graph between 1 and 9 seconds. By counting the number of squares, we can estimate the area to be approximately 24 square units. Since each square represents a velocity of 10 km/h and the time interval is 8 seconds, the distance traveled by the car is approximately 240 km.
b. The average speed of the car between 1 and 9 seconds is equal to the total distance traveled divided by the time taken, which is 240 km / 8 s = 30 km/s.
c. The speed of the car increases from 0 km/h to 60 km/h in the first 2 seconds, then remains constant at 60 km/h for the next 6 seconds, and finally decreases to 0 km/h in the last 2 seconds. Therefore, the speed of the car changes from increasing to constant to decreasing throughout its test run.
d. If we had a graph of velocity versus time for this test, the total area under the curve would represent the total displacement of the car, which is equal to the distance traveled in this case. Since the area under the curve is a trapezoid, we can calculate it as the average of the two parallel sides multiplied by the height, which is (0 + 60) / 2 x 8 = 240 km/s.
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